A091656 Least number k such that the continued fraction expansion of H(k) contains the numbers 1, 2, ..., n, where H(k) is the k-th Harmonic number.

1, 2, 5, 9, 9, 13, 26, 63, 68, 68, 68, 87, 121, 121, 165, 207, 207, 221, 221, 287, 289, 325, 428, 440, 483, 544, 544, 544, 544, 544, 558, 558, 558, 966, 1035, 1035, 1146, 1146, 1332, 1332, 1332, 1665, 1665, 1665, 1665, 1665, 1727, 1727, 2052, 2157, 2331, 2331

Offset

1,2

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..250

Example

a(6) = 13 because CF( H(13)) = 3 + [5, 1, 1, 4, 2, 1, 3, 2, 1, 3, 1, 4, 1, 6], the first six integers are present.

Mathematica

f[n_] := Block[{k = 1}, While[ StringPosition[ ToString[ Union[ ContinuedFraction[ Sum[1/i, {i, 1, k}]]]], StringDrop[ ToString[ Table[i, {i, n}]], -1]] == {}, k++ ]; k]; Table[ f[n], {n, 1, 52}]

Prog

(PARI) list(lim)=my(v=vector(lim\1), n, t, H, i=1); while(1, H+=1/n++; t=vecsort(contfrac(H), , 8); if(#t>=i&&t[i]==i, v[i]=n; print1(n":"i", "); if(i++>#v, return(v)); H-=1/n; n--)) \\ Charles R Greathouse IV, Jan 25 2012

Crossrefs

Cf. A055573, A091655.

Sequence in context: A129140 A002580 A196408 * A273044 A133508 A125969

Adjacent sequences: A091653 A091654 A091655 * A091657 A091658 A091659

Keyword

nonn

Author

Robert G. Wilson v, Jan 26 2004

Status

approved